In a sonometer experiment the bridges are separted by a fixed distance the wire which is slightly elastic emits a tone of frequency n when held by tension T If the tension is increased to 4T the tone emitted by the wire will be of frequency

Options

A. n
B. 2n
C. slightly greater than 2n
D. slightly less than 2n

Answer

d

Explanation

Frequency of wave produced in the wire
`n=1/2 xxsqrt(T)/(mu)`
where I = length of the wire
`mu` = mass per unit length
T= tension in the wire

Frequency produced when tension changes to T
`n=1/(2I)xxsqrt(T)/(mu) rarr n =(1)/(2I)xxssqrt(4T)/(mu)`...(ii)
on divinding E (i) by Eq (ii) we get
`(n)/(n)=sqrt(1/4)=1/2 rarr n=2n`